1/****************************************************************************** 2 * * 3 * Copyright 2014 Intel Corporation * 4 * * 5 * Licensed under the Apache License, Version 2.0 (the "License"); * 6 * you may not use this file except in compliance with the License. * 7 * You may obtain a copy of the License at * 8 * * 9 * http://www.apache.org/licenses/LICENSE-2.0 * 10 * * 11 * Unless required by applicable law or agreed to in writing, software * 12 * distributed under the License is distributed on an "AS IS" BASIS, * 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * 14 * See the License for the specific language governing permissions and * 15 * limitations under the License. * 16 * * 17 ****************************************************************************** 18 * * 19 * Developers and authors: * 20 * Shay Gueron (1, 2), and Vlad Krasnov (1) * 21 * (1) Intel Corporation, Israel Development Center * 22 * (2) University of Haifa * 23 * Reference: * 24 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with * 25 * 256 Bit Primes" * 26 * * 27 ******************************************************************************/ 28 29#include <string.h> 30 31#include <openssl/bn.h> 32#include <openssl/err.h> 33#include <openssl/ec.h> 34#include "cryptlib.h" 35 36#include "ec_lcl.h" 37 38#if BN_BITS2 != 64 39# define TOBN(hi,lo) lo,hi 40#else 41# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo) 42#endif 43 44#if defined(__GNUC__) 45# define ALIGN32 __attribute((aligned(32))) 46#elif defined(_MSC_VER) 47# define ALIGN32 __declspec(align(32)) 48#else 49# define ALIGN32 50#endif 51 52#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N) 53#define P256_LIMBS (256/BN_BITS2) 54 55typedef unsigned short u16; 56 57typedef struct { 58 BN_ULONG X[P256_LIMBS]; 59 BN_ULONG Y[P256_LIMBS]; 60 BN_ULONG Z[P256_LIMBS]; 61} P256_POINT; 62 63typedef struct { 64 BN_ULONG X[P256_LIMBS]; 65 BN_ULONG Y[P256_LIMBS]; 66} P256_POINT_AFFINE; 67 68typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; 69 70/* structure for precomputed multiples of the generator */ 71typedef struct ec_pre_comp_st { 72 const EC_GROUP *group; /* Parent EC_GROUP object */ 73 size_t w; /* Window size */ 74 /* 75 * Constant time access to the X and Y coordinates of the pre-computed, 76 * generator multiplies, in the Montgomery domain. Pre-calculated 77 * multiplies are stored in affine form. 78 */ 79 PRECOMP256_ROW *precomp; 80 void *precomp_storage; 81 int references; 82} EC_PRE_COMP; 83 84/* Functions implemented in assembly */ 85/* Modular mul by 2: res = 2*a mod P */ 86void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS], 87 const BN_ULONG a[P256_LIMBS]); 88/* Modular div by 2: res = a/2 mod P */ 89void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], 90 const BN_ULONG a[P256_LIMBS]); 91/* Modular mul by 3: res = 3*a mod P */ 92void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], 93 const BN_ULONG a[P256_LIMBS]); 94/* Modular add: res = a+b mod P */ 95void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], 96 const BN_ULONG a[P256_LIMBS], 97 const BN_ULONG b[P256_LIMBS]); 98/* Modular sub: res = a-b mod P */ 99void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], 100 const BN_ULONG a[P256_LIMBS], 101 const BN_ULONG b[P256_LIMBS]); 102/* Modular neg: res = -a mod P */ 103void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); 104/* Montgomery mul: res = a*b*2^-256 mod P */ 105void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS], 106 const BN_ULONG a[P256_LIMBS], 107 const BN_ULONG b[P256_LIMBS]); 108/* Montgomery sqr: res = a*a*2^-256 mod P */ 109void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS], 110 const BN_ULONG a[P256_LIMBS]); 111/* Convert a number from Montgomery domain, by multiplying with 1 */ 112void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS], 113 const BN_ULONG in[P256_LIMBS]); 114/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/ 115void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS], 116 const BN_ULONG in[P256_LIMBS]); 117/* Functions that perform constant time access to the precomputed tables */ 118void ecp_nistz256_select_w5(P256_POINT * val, 119 const P256_POINT * in_t, int index); 120void ecp_nistz256_select_w7(P256_POINT_AFFINE * val, 121 const P256_POINT_AFFINE * in_t, int index); 122 123/* One converted into the Montgomery domain */ 124static const BN_ULONG ONE[P256_LIMBS] = { 125 TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), 126 TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe) 127}; 128 129static void *ecp_nistz256_pre_comp_dup(void *); 130static void ecp_nistz256_pre_comp_free(void *); 131static void ecp_nistz256_pre_comp_clear_free(void *); 132static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); 133 134/* Precomputed tables for the default generator */ 135#include "ecp_nistz256_table.c" 136 137/* Recode window to a signed digit, see ecp_nistputil.c for details */ 138static unsigned int _booth_recode_w5(unsigned int in) 139{ 140 unsigned int s, d; 141 142 s = ~((in >> 5) - 1); 143 d = (1 << 6) - in - 1; 144 d = (d & s) | (in & ~s); 145 d = (d >> 1) + (d & 1); 146 147 return (d << 1) + (s & 1); 148} 149 150static unsigned int _booth_recode_w7(unsigned int in) 151{ 152 unsigned int s, d; 153 154 s = ~((in >> 7) - 1); 155 d = (1 << 8) - in - 1; 156 d = (d & s) | (in & ~s); 157 d = (d >> 1) + (d & 1); 158 159 return (d << 1) + (s & 1); 160} 161 162static void copy_conditional(BN_ULONG dst[P256_LIMBS], 163 const BN_ULONG src[P256_LIMBS], BN_ULONG move) 164{ 165 BN_ULONG mask1 = -move; 166 BN_ULONG mask2 = ~mask1; 167 168 dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); 169 dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); 170 dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); 171 dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); 172 if (P256_LIMBS == 8) { 173 dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); 174 dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); 175 dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); 176 dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); 177 } 178} 179 180static BN_ULONG is_zero(BN_ULONG in) 181{ 182 in |= (0 - in); 183 in = ~in; 184 in &= BN_MASK2; 185 in >>= BN_BITS2 - 1; 186 return in; 187} 188 189static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], 190 const BN_ULONG b[P256_LIMBS]) 191{ 192 BN_ULONG res; 193 194 res = a[0] ^ b[0]; 195 res |= a[1] ^ b[1]; 196 res |= a[2] ^ b[2]; 197 res |= a[3] ^ b[3]; 198 if (P256_LIMBS == 8) { 199 res |= a[4] ^ b[4]; 200 res |= a[5] ^ b[5]; 201 res |= a[6] ^ b[6]; 202 res |= a[7] ^ b[7]; 203 } 204 205 return is_zero(res); 206} 207 208static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS]) 209{ 210 BN_ULONG res; 211 212 res = a[0] ^ ONE[0]; 213 res |= a[1] ^ ONE[1]; 214 res |= a[2] ^ ONE[2]; 215 res |= a[3] ^ ONE[3]; 216 if (P256_LIMBS == 8) { 217 res |= a[4] ^ ONE[4]; 218 res |= a[5] ^ ONE[5]; 219 res |= a[6] ^ ONE[6]; 220 } 221 222 return is_zero(res); 223} 224 225static int ecp_nistz256_set_words(BIGNUM *a, BN_ULONG words[P256_LIMBS]) 226 { 227 if (bn_wexpand(a, P256_LIMBS) == NULL) { 228 ECerr(EC_F_ECP_NISTZ256_SET_WORDS, ERR_R_MALLOC_FAILURE); 229 return 0; 230 } 231 memcpy(a->d, words, sizeof(BN_ULONG) * P256_LIMBS); 232 a->top = P256_LIMBS; 233 bn_correct_top(a); 234 return 1; 235} 236 237#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION 238void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a); 239void ecp_nistz256_point_add(P256_POINT *r, 240 const P256_POINT *a, const P256_POINT *b); 241void ecp_nistz256_point_add_affine(P256_POINT *r, 242 const P256_POINT *a, 243 const P256_POINT_AFFINE *b); 244#else 245/* Point double: r = 2*a */ 246static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a) 247{ 248 BN_ULONG S[P256_LIMBS]; 249 BN_ULONG M[P256_LIMBS]; 250 BN_ULONG Zsqr[P256_LIMBS]; 251 BN_ULONG tmp0[P256_LIMBS]; 252 253 const BN_ULONG *in_x = a->X; 254 const BN_ULONG *in_y = a->Y; 255 const BN_ULONG *in_z = a->Z; 256 257 BN_ULONG *res_x = r->X; 258 BN_ULONG *res_y = r->Y; 259 BN_ULONG *res_z = r->Z; 260 261 ecp_nistz256_mul_by_2(S, in_y); 262 263 ecp_nistz256_sqr_mont(Zsqr, in_z); 264 265 ecp_nistz256_sqr_mont(S, S); 266 267 ecp_nistz256_mul_mont(res_z, in_z, in_y); 268 ecp_nistz256_mul_by_2(res_z, res_z); 269 270 ecp_nistz256_add(M, in_x, Zsqr); 271 ecp_nistz256_sub(Zsqr, in_x, Zsqr); 272 273 ecp_nistz256_sqr_mont(res_y, S); 274 ecp_nistz256_div_by_2(res_y, res_y); 275 276 ecp_nistz256_mul_mont(M, M, Zsqr); 277 ecp_nistz256_mul_by_3(M, M); 278 279 ecp_nistz256_mul_mont(S, S, in_x); 280 ecp_nistz256_mul_by_2(tmp0, S); 281 282 ecp_nistz256_sqr_mont(res_x, M); 283 284 ecp_nistz256_sub(res_x, res_x, tmp0); 285 ecp_nistz256_sub(S, S, res_x); 286 287 ecp_nistz256_mul_mont(S, S, M); 288 ecp_nistz256_sub(res_y, S, res_y); 289} 290 291/* Point addition: r = a+b */ 292static void ecp_nistz256_point_add(P256_POINT *r, 293 const P256_POINT *a, const P256_POINT *b) 294{ 295 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; 296 BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS]; 297 BN_ULONG Z1sqr[P256_LIMBS]; 298 BN_ULONG Z2sqr[P256_LIMBS]; 299 BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; 300 BN_ULONG Hsqr[P256_LIMBS]; 301 BN_ULONG Rsqr[P256_LIMBS]; 302 BN_ULONG Hcub[P256_LIMBS]; 303 304 BN_ULONG res_x[P256_LIMBS]; 305 BN_ULONG res_y[P256_LIMBS]; 306 BN_ULONG res_z[P256_LIMBS]; 307 308 BN_ULONG in1infty, in2infty; 309 310 const BN_ULONG *in1_x = a->X; 311 const BN_ULONG *in1_y = a->Y; 312 const BN_ULONG *in1_z = a->Z; 313 314 const BN_ULONG *in2_x = b->X; 315 const BN_ULONG *in2_y = b->Y; 316 const BN_ULONG *in2_z = b->Z; 317 318 /* We encode infinity as (0,0), which is not on the curve, 319 * so it is OK. */ 320 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] | 321 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]); 322 if (P256_LIMBS == 8) 323 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] | 324 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]); 325 326 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | 327 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); 328 if (P256_LIMBS == 8) 329 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | 330 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); 331 332 in1infty = is_zero(in1infty); 333 in2infty = is_zero(in2infty); 334 335 ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */ 336 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ 337 338 ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ 339 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ 340 341 ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ 342 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ 343 ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */ 344 345 ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ 346 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ 347 ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ 348 349 /* 350 * This should not happen during sign/ecdh, so no constant time violation 351 */ 352 if (is_equal(U1, U2) && !in1infty && !in2infty) { 353 if (is_equal(S1, S2)) { 354 ecp_nistz256_point_double(r, a); 355 return; 356 } else { 357 memset(r, 0, sizeof(*r)); 358 return; 359 } 360 } 361 362 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ 363 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ 364 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ 365 ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ 366 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ 367 368 ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */ 369 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ 370 371 ecp_nistz256_sub(res_x, Rsqr, Hsqr); 372 ecp_nistz256_sub(res_x, res_x, Hcub); 373 374 ecp_nistz256_sub(res_y, U2, res_x); 375 376 ecp_nistz256_mul_mont(S2, S1, Hcub); 377 ecp_nistz256_mul_mont(res_y, R, res_y); 378 ecp_nistz256_sub(res_y, res_y, S2); 379 380 copy_conditional(res_x, in2_x, in1infty); 381 copy_conditional(res_y, in2_y, in1infty); 382 copy_conditional(res_z, in2_z, in1infty); 383 384 copy_conditional(res_x, in1_x, in2infty); 385 copy_conditional(res_y, in1_y, in2infty); 386 copy_conditional(res_z, in1_z, in2infty); 387 388 memcpy(r->X, res_x, sizeof(res_x)); 389 memcpy(r->Y, res_y, sizeof(res_y)); 390 memcpy(r->Z, res_z, sizeof(res_z)); 391} 392 393/* Point addition when b is known to be affine: r = a+b */ 394static void ecp_nistz256_point_add_affine(P256_POINT *r, 395 const P256_POINT *a, 396 const P256_POINT_AFFINE *b) 397{ 398 BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; 399 BN_ULONG Z1sqr[P256_LIMBS]; 400 BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; 401 BN_ULONG Hsqr[P256_LIMBS]; 402 BN_ULONG Rsqr[P256_LIMBS]; 403 BN_ULONG Hcub[P256_LIMBS]; 404 405 BN_ULONG res_x[P256_LIMBS]; 406 BN_ULONG res_y[P256_LIMBS]; 407 BN_ULONG res_z[P256_LIMBS]; 408 409 BN_ULONG in1infty, in2infty; 410 411 const BN_ULONG *in1_x = a->X; 412 const BN_ULONG *in1_y = a->Y; 413 const BN_ULONG *in1_z = a->Z; 414 415 const BN_ULONG *in2_x = b->X; 416 const BN_ULONG *in2_y = b->Y; 417 418 /* 419 * In affine representation we encode infty as (0,0), which is not on the 420 * curve, so it is OK 421 */ 422 in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] | 423 in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]); 424 if (P256_LIMBS == 8) 425 in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] | 426 in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]); 427 428 in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | 429 in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); 430 if (P256_LIMBS == 8) 431 in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | 432 in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); 433 434 in1infty = is_zero(in1infty); 435 in2infty = is_zero(in2infty); 436 437 ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ 438 439 ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ 440 ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */ 441 442 ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ 443 444 ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ 445 446 ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ 447 ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */ 448 449 ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ 450 ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ 451 ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ 452 453 ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */ 454 ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ 455 456 ecp_nistz256_sub(res_x, Rsqr, Hsqr); 457 ecp_nistz256_sub(res_x, res_x, Hcub); 458 ecp_nistz256_sub(H, U2, res_x); 459 460 ecp_nistz256_mul_mont(S2, in1_y, Hcub); 461 ecp_nistz256_mul_mont(H, H, R); 462 ecp_nistz256_sub(res_y, H, S2); 463 464 copy_conditional(res_x, in2_x, in1infty); 465 copy_conditional(res_x, in1_x, in2infty); 466 467 copy_conditional(res_y, in2_y, in1infty); 468 copy_conditional(res_y, in1_y, in2infty); 469 470 copy_conditional(res_z, ONE, in1infty); 471 copy_conditional(res_z, in1_z, in2infty); 472 473 memcpy(r->X, res_x, sizeof(res_x)); 474 memcpy(r->Y, res_y, sizeof(res_y)); 475 memcpy(r->Z, res_z, sizeof(res_z)); 476} 477#endif 478 479/* r = in^-1 mod p */ 480static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS], 481 const BN_ULONG in[P256_LIMBS]) 482{ 483 /* 484 * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff 485 * ffffffff ffffffff We use FLT and used poly-2 as exponent 486 */ 487 BN_ULONG p2[P256_LIMBS]; 488 BN_ULONG p4[P256_LIMBS]; 489 BN_ULONG p8[P256_LIMBS]; 490 BN_ULONG p16[P256_LIMBS]; 491 BN_ULONG p32[P256_LIMBS]; 492 BN_ULONG res[P256_LIMBS]; 493 int i; 494 495 ecp_nistz256_sqr_mont(res, in); 496 ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ 497 498 ecp_nistz256_sqr_mont(res, p2); 499 ecp_nistz256_sqr_mont(res, res); 500 ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ 501 502 ecp_nistz256_sqr_mont(res, p4); 503 ecp_nistz256_sqr_mont(res, res); 504 ecp_nistz256_sqr_mont(res, res); 505 ecp_nistz256_sqr_mont(res, res); 506 ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ 507 508 ecp_nistz256_sqr_mont(res, p8); 509 for (i = 0; i < 7; i++) 510 ecp_nistz256_sqr_mont(res, res); 511 ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ 512 513 ecp_nistz256_sqr_mont(res, p16); 514 for (i = 0; i < 15; i++) 515 ecp_nistz256_sqr_mont(res, res); 516 ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ 517 518 ecp_nistz256_sqr_mont(res, p32); 519 for (i = 0; i < 31; i++) 520 ecp_nistz256_sqr_mont(res, res); 521 ecp_nistz256_mul_mont(res, res, in); 522 523 for (i = 0; i < 32 * 4; i++) 524 ecp_nistz256_sqr_mont(res, res); 525 ecp_nistz256_mul_mont(res, res, p32); 526 527 for (i = 0; i < 32; i++) 528 ecp_nistz256_sqr_mont(res, res); 529 ecp_nistz256_mul_mont(res, res, p32); 530 531 for (i = 0; i < 16; i++) 532 ecp_nistz256_sqr_mont(res, res); 533 ecp_nistz256_mul_mont(res, res, p16); 534 535 for (i = 0; i < 8; i++) 536 ecp_nistz256_sqr_mont(res, res); 537 ecp_nistz256_mul_mont(res, res, p8); 538 539 ecp_nistz256_sqr_mont(res, res); 540 ecp_nistz256_sqr_mont(res, res); 541 ecp_nistz256_sqr_mont(res, res); 542 ecp_nistz256_sqr_mont(res, res); 543 ecp_nistz256_mul_mont(res, res, p4); 544 545 ecp_nistz256_sqr_mont(res, res); 546 ecp_nistz256_sqr_mont(res, res); 547 ecp_nistz256_mul_mont(res, res, p2); 548 549 ecp_nistz256_sqr_mont(res, res); 550 ecp_nistz256_sqr_mont(res, res); 551 ecp_nistz256_mul_mont(res, res, in); 552 553 memcpy(r, res, sizeof(res)); 554} 555 556/* 557 * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and 558 * returns one if it fits. Otherwise it returns zero. 559 */ 560static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], 561 const BIGNUM *in) 562{ 563 if (in->top > P256_LIMBS) 564 return 0; 565 566 memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS); 567 memcpy(out, in->d, sizeof(BN_ULONG) * in->top); 568 return 1; 569} 570 571/* r = sum(scalar[i]*point[i]) */ 572static int ecp_nistz256_windowed_mul(const EC_GROUP *group, 573 P256_POINT *r, 574 const BIGNUM **scalar, 575 const EC_POINT **point, 576 int num, BN_CTX *ctx) 577{ 578 579 int i, j, ret = 0; 580 unsigned int index; 581 unsigned char (*p_str)[33] = NULL; 582 const unsigned int window_size = 5; 583 const unsigned int mask = (1 << (window_size + 1)) - 1; 584 unsigned int wvalue; 585 BN_ULONG tmp[P256_LIMBS]; 586 ALIGN32 P256_POINT h; 587 const BIGNUM **scalars = NULL; 588 P256_POINT (*table)[16] = NULL; 589 void *table_storage = NULL; 590 591 if ((table_storage = 592 OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64)) == NULL 593 || (p_str = 594 OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL 595 || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { 596 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE); 597 goto err; 598 } else { 599 table = (void *)ALIGNPTR(table_storage, 64); 600 } 601 602 for (i = 0; i < num; i++) { 603 P256_POINT *row = table[i]; 604 605 /* This is an unusual input, we don't guarantee constant-timeness. */ 606 if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { 607 BIGNUM *mod; 608 609 if ((mod = BN_CTX_get(ctx)) == NULL) 610 goto err; 611 if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) { 612 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB); 613 goto err; 614 } 615 scalars[i] = mod; 616 } else 617 scalars[i] = scalar[i]; 618 619 for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) { 620 BN_ULONG d = scalars[i]->d[j / BN_BYTES]; 621 622 p_str[i][j + 0] = d & 0xff; 623 p_str[i][j + 1] = (d >> 8) & 0xff; 624 p_str[i][j + 2] = (d >> 16) & 0xff; 625 p_str[i][j + 3] = (d >>= 24) & 0xff; 626 if (BN_BYTES == 8) { 627 d >>= 8; 628 p_str[i][j + 4] = d & 0xff; 629 p_str[i][j + 5] = (d >> 8) & 0xff; 630 p_str[i][j + 6] = (d >> 16) & 0xff; 631 p_str[i][j + 7] = (d >> 24) & 0xff; 632 } 633 } 634 for (; j < 33; j++) 635 p_str[i][j] = 0; 636 637 /* table[0] is implicitly (0,0,0) (the point at infinity), 638 * therefore it is not stored. All other values are actually 639 * stored with an offset of -1 in table. 640 */ 641 642 if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &point[i]->X) 643 || !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &point[i]->Y) 644 || !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &point[i]->Z)) { 645 ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE); 646 goto err; 647 } 648 649 ecp_nistz256_point_double(&row[ 2 - 1], &row[ 1 - 1]); 650 ecp_nistz256_point_add (&row[ 3 - 1], &row[ 2 - 1], &row[1 - 1]); 651 ecp_nistz256_point_double(&row[ 4 - 1], &row[ 2 - 1]); 652 ecp_nistz256_point_double(&row[ 6 - 1], &row[ 3 - 1]); 653 ecp_nistz256_point_double(&row[ 8 - 1], &row[ 4 - 1]); 654 ecp_nistz256_point_double(&row[12 - 1], &row[ 6 - 1]); 655 ecp_nistz256_point_add (&row[ 5 - 1], &row[ 4 - 1], &row[1 - 1]); 656 ecp_nistz256_point_add (&row[ 7 - 1], &row[ 6 - 1], &row[1 - 1]); 657 ecp_nistz256_point_add (&row[ 9 - 1], &row[ 8 - 1], &row[1 - 1]); 658 ecp_nistz256_point_add (&row[13 - 1], &row[12 - 1], &row[1 - 1]); 659 ecp_nistz256_point_double(&row[14 - 1], &row[ 7 - 1]); 660 ecp_nistz256_point_double(&row[10 - 1], &row[ 5 - 1]); 661 ecp_nistz256_point_add (&row[15 - 1], &row[14 - 1], &row[1 - 1]); 662 ecp_nistz256_point_add (&row[11 - 1], &row[10 - 1], &row[1 - 1]); 663 ecp_nistz256_point_add (&row[16 - 1], &row[15 - 1], &row[1 - 1]); 664 } 665 666 index = 255; 667 668 wvalue = p_str[0][(index - 1) / 8]; 669 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 670 671 ecp_nistz256_select_w5(r, table[0], _booth_recode_w5(wvalue) >> 1); 672 673 while (index >= 5) { 674 for (i = (index == 255 ? 1 : 0); i < num; i++) { 675 unsigned int off = (index - 1) / 8; 676 677 wvalue = p_str[i][off] | p_str[i][off + 1] << 8; 678 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 679 680 wvalue = _booth_recode_w5(wvalue); 681 682 ecp_nistz256_select_w5(&h, table[i], wvalue >> 1); 683 684 ecp_nistz256_neg(tmp, h.Y); 685 copy_conditional(h.Y, tmp, (wvalue & 1)); 686 687 ecp_nistz256_point_add(r, r, &h); 688 } 689 690 index -= window_size; 691 692 ecp_nistz256_point_double(r, r); 693 ecp_nistz256_point_double(r, r); 694 ecp_nistz256_point_double(r, r); 695 ecp_nistz256_point_double(r, r); 696 ecp_nistz256_point_double(r, r); 697 } 698 699 /* Final window */ 700 for (i = 0; i < num; i++) { 701 wvalue = p_str[i][0]; 702 wvalue = (wvalue << 1) & mask; 703 704 wvalue = _booth_recode_w5(wvalue); 705 706 ecp_nistz256_select_w5(&h, table[i], wvalue >> 1); 707 708 ecp_nistz256_neg(tmp, h.Y); 709 copy_conditional(h.Y, tmp, wvalue & 1); 710 711 ecp_nistz256_point_add(r, r, &h); 712 } 713 714 ret = 1; 715 err: 716 if (table_storage) 717 OPENSSL_free(table_storage); 718 if (p_str) 719 OPENSSL_free(p_str); 720 if (scalars) 721 OPENSSL_free(scalars); 722 return ret; 723} 724 725/* Coordinates of G, for which we have precomputed tables */ 726const static BN_ULONG def_xG[P256_LIMBS] = { 727 TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), 728 TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6) 729}; 730 731const static BN_ULONG def_yG[P256_LIMBS] = { 732 TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), 733 TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) 734}; 735 736/* 737 * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256 738 * generator. 739 */ 740static int ecp_nistz256_is_affine_G(const EC_POINT *generator) 741{ 742 return (generator->X.top == P256_LIMBS) && 743 (generator->Y.top == P256_LIMBS) && 744 (generator->Z.top == (P256_LIMBS - P256_LIMBS / 8)) && 745 is_equal(generator->X.d, def_xG) && 746 is_equal(generator->Y.d, def_yG) && is_one(generator->Z.d); 747} 748 749static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) 750{ 751 /* 752 * We precompute a table for a Booth encoded exponent (wNAF) based 753 * computation. Each table holds 64 values for safe access, with an 754 * implicit value of infinity at index zero. We use window of size 7, and 755 * therefore require ceil(256/7) = 37 tables. 756 */ 757 BIGNUM *order; 758 EC_POINT *P = NULL, *T = NULL; 759 const EC_POINT *generator; 760 EC_PRE_COMP *pre_comp; 761 BN_CTX *new_ctx = NULL; 762 int i, j, k, ret = 0; 763 size_t w; 764 765 PRECOMP256_ROW *preComputedTable = NULL; 766 unsigned char *precomp_storage = NULL; 767 768 /* if there is an old EC_PRE_COMP object, throw it away */ 769 EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup, 770 ecp_nistz256_pre_comp_free, 771 ecp_nistz256_pre_comp_clear_free); 772 773 generator = EC_GROUP_get0_generator(group); 774 if (generator == NULL) { 775 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR); 776 return 0; 777 } 778 779 if (ecp_nistz256_is_affine_G(generator)) { 780 /* 781 * No need to calculate tables for the standard generator because we 782 * have them statically. 783 */ 784 return 1; 785 } 786 787 if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL) 788 return 0; 789 790 if (ctx == NULL) { 791 ctx = new_ctx = BN_CTX_new(); 792 if (ctx == NULL) 793 goto err; 794 } 795 796 BN_CTX_start(ctx); 797 order = BN_CTX_get(ctx); 798 799 if (order == NULL) 800 goto err; 801 802 if (!EC_GROUP_get_order(group, order, ctx)) 803 goto err; 804 805 if (BN_is_zero(order)) { 806 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER); 807 goto err; 808 } 809 810 w = 7; 811 812 if ((precomp_storage = 813 OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) { 814 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE); 815 goto err; 816 } else { 817 preComputedTable = (void *)ALIGNPTR(precomp_storage, 64); 818 } 819 820 P = EC_POINT_new(group); 821 T = EC_POINT_new(group); 822 if (P == NULL || T == NULL) 823 goto err; 824 825 /* 826 * The zero entry is implicitly infinity, and we skip it, storing other 827 * values with -1 offset. 828 */ 829 if (!EC_POINT_copy(T, generator)) 830 goto err; 831 832 for (k = 0; k < 64; k++) { 833 if (!EC_POINT_copy(P, T)) 834 goto err; 835 for (j = 0; j < 37; j++) { 836 /* 837 * It would be faster to use EC_POINTs_make_affine and 838 * make multiple points affine at the same time. 839 */ 840 if (!EC_POINT_make_affine(group, P, ctx)) 841 goto err; 842 if (!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].X, 843 &P->X) || 844 !ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].Y, 845 &P->Y)) { 846 ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, 847 EC_R_COORDINATES_OUT_OF_RANGE); 848 goto err; 849 } 850 for (i = 0; i < 7; i++) { 851 if (!EC_POINT_dbl(group, P, P, ctx)) 852 goto err; 853 } 854 } 855 if (!EC_POINT_add(group, T, T, generator, ctx)) 856 goto err; 857 } 858 859 pre_comp->group = group; 860 pre_comp->w = w; 861 pre_comp->precomp = preComputedTable; 862 pre_comp->precomp_storage = precomp_storage; 863 864 precomp_storage = NULL; 865 866 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, 867 ecp_nistz256_pre_comp_dup, 868 ecp_nistz256_pre_comp_free, 869 ecp_nistz256_pre_comp_clear_free)) { 870 goto err; 871 } 872 873 pre_comp = NULL; 874 875 ret = 1; 876 877 err: 878 if (ctx != NULL) 879 BN_CTX_end(ctx); 880 BN_CTX_free(new_ctx); 881 882 if (pre_comp) 883 ecp_nistz256_pre_comp_free(pre_comp); 884 if (precomp_storage) 885 OPENSSL_free(precomp_storage); 886 if (P) 887 EC_POINT_free(P); 888 if (T) 889 EC_POINT_free(T); 890 return ret; 891} 892 893/* 894 * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great 895 * code processing 4 points in parallel, corresponding serial operation 896 * is several times slower, because it uses 29x29=58-bit multiplication 897 * as opposite to 64x64=128-bit in integer-only scalar case. As result 898 * it doesn't provide *significant* performance improvement. Note that 899 * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work, 900 * you'd need to compile even asm/ecp_nistz256-avx.pl module. 901 */ 902#if defined(ECP_NISTZ256_AVX2) 903# if !(defined(__x86_64) || defined(__x86_64__)) || \ 904 defined(_M_AMD64) || defined(_MX64)) || \ 905 !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */ 906# undef ECP_NISTZ256_AVX2 907# else 908/* Constant time access, loading four values, from four consecutive tables */ 909void ecp_nistz256_avx2_select_w7(P256_POINT_AFFINE * val, 910 const P256_POINT_AFFINE * in_t, int index); 911void ecp_nistz256_avx2_multi_select_w7(void *result, const void *in, int index0, 912 int index1, int index2, int index3); 913void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in); 914void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4); 915void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4, 916 const void *Bx4); 917void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4, 918 const void *Bx4); 919void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4); 920void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4); 921void ecp_nistz256_avx2_set1(void *RESULTx4); 922int ecp_nistz_avx2_eligible(void); 923 924static void booth_recode_w7(unsigned char *sign, 925 unsigned char *digit, unsigned char in) 926{ 927 unsigned char s, d; 928 929 s = ~((in >> 7) - 1); 930 d = (1 << 8) - in - 1; 931 d = (d & s) | (in & ~s); 932 d = (d >> 1) + (d & 1); 933 934 *sign = s & 1; 935 *digit = d; 936} 937 938/* 939 * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the 940 * precomputed table. It does 4 affine point additions in parallel, 941 * significantly speeding up point multiplication for a fixed value. 942 */ 943static void ecp_nistz256_avx2_mul_g(P256_POINT *r, 944 unsigned char p_str[33], 945 const P256_POINT_AFFINE(*preComputedTable)[64]) 946{ 947 const unsigned int window_size = 7; 948 const unsigned int mask = (1 << (window_size + 1)) - 1; 949 unsigned int wvalue; 950 /* Using 4 windows at a time */ 951 unsigned char sign0, digit0; 952 unsigned char sign1, digit1; 953 unsigned char sign2, digit2; 954 unsigned char sign3, digit3; 955 unsigned int index = 0; 956 BN_ULONG tmp[P256_LIMBS]; 957 int i; 958 959 ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 }; 960 ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 }; 961 ALIGN32 P256_POINT_AFFINE point_arr[P256_LIMBS]; 962 ALIGN32 P256_POINT res_point_arr[P256_LIMBS]; 963 964 /* Initial four windows */ 965 wvalue = *((u16 *) & p_str[0]); 966 wvalue = (wvalue << 1) & mask; 967 index += window_size; 968 booth_recode_w7(&sign0, &digit0, wvalue); 969 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 970 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 971 index += window_size; 972 booth_recode_w7(&sign1, &digit1, wvalue); 973 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 974 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 975 index += window_size; 976 booth_recode_w7(&sign2, &digit2, wvalue); 977 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 978 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 979 index += window_size; 980 booth_recode_w7(&sign3, &digit3, wvalue); 981 982 ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[0], 983 digit0, digit1, digit2, digit3); 984 985 ecp_nistz256_neg(tmp, point_arr[0].Y); 986 copy_conditional(point_arr[0].Y, tmp, sign0); 987 ecp_nistz256_neg(tmp, point_arr[1].Y); 988 copy_conditional(point_arr[1].Y, tmp, sign1); 989 ecp_nistz256_neg(tmp, point_arr[2].Y); 990 copy_conditional(point_arr[2].Y, tmp, sign2); 991 ecp_nistz256_neg(tmp, point_arr[3].Y); 992 copy_conditional(point_arr[3].Y, tmp, sign3); 993 994 ecp_nistz256_avx2_transpose_convert(aX4, point_arr); 995 ecp_nistz256_avx2_to_mont(aX4, aX4); 996 ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]); 997 ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]); 998 999 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1000 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1001 index += window_size; 1002 booth_recode_w7(&sign0, &digit0, wvalue); 1003 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1004 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1005 index += window_size; 1006 booth_recode_w7(&sign1, &digit1, wvalue); 1007 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1008 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1009 index += window_size; 1010 booth_recode_w7(&sign2, &digit2, wvalue); 1011 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1012 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1013 index += window_size; 1014 booth_recode_w7(&sign3, &digit3, wvalue); 1015 1016 ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[4 * 1], 1017 digit0, digit1, digit2, digit3); 1018 1019 ecp_nistz256_neg(tmp, point_arr[0].Y); 1020 copy_conditional(point_arr[0].Y, tmp, sign0); 1021 ecp_nistz256_neg(tmp, point_arr[1].Y); 1022 copy_conditional(point_arr[1].Y, tmp, sign1); 1023 ecp_nistz256_neg(tmp, point_arr[2].Y); 1024 copy_conditional(point_arr[2].Y, tmp, sign2); 1025 ecp_nistz256_neg(tmp, point_arr[3].Y); 1026 copy_conditional(point_arr[3].Y, tmp, sign3); 1027 1028 ecp_nistz256_avx2_transpose_convert(bX4, point_arr); 1029 ecp_nistz256_avx2_to_mont(bX4, bX4); 1030 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); 1031 /* Optimized when both inputs are affine */ 1032 ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4); 1033 1034 for (i = 2; i < 9; i++) { 1035 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1036 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1037 index += window_size; 1038 booth_recode_w7(&sign0, &digit0, wvalue); 1039 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1040 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1041 index += window_size; 1042 booth_recode_w7(&sign1, &digit1, wvalue); 1043 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1044 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1045 index += window_size; 1046 booth_recode_w7(&sign2, &digit2, wvalue); 1047 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1048 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1049 index += window_size; 1050 booth_recode_w7(&sign3, &digit3, wvalue); 1051 1052 ecp_nistz256_avx2_multi_select_w7(point_arr, 1053 preComputedTable[4 * i], 1054 digit0, digit1, digit2, digit3); 1055 1056 ecp_nistz256_neg(tmp, point_arr[0].Y); 1057 copy_conditional(point_arr[0].Y, tmp, sign0); 1058 ecp_nistz256_neg(tmp, point_arr[1].Y); 1059 copy_conditional(point_arr[1].Y, tmp, sign1); 1060 ecp_nistz256_neg(tmp, point_arr[2].Y); 1061 copy_conditional(point_arr[2].Y, tmp, sign2); 1062 ecp_nistz256_neg(tmp, point_arr[3].Y); 1063 copy_conditional(point_arr[3].Y, tmp, sign3); 1064 1065 ecp_nistz256_avx2_transpose_convert(bX4, point_arr); 1066 ecp_nistz256_avx2_to_mont(bX4, bX4); 1067 ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); 1068 1069 ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4); 1070 } 1071 1072 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]); 1073 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]); 1074 ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]); 1075 1076 ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4); 1077 /* Last window is performed serially */ 1078 wvalue = *((u16 *) & p_str[(index - 1) / 8]); 1079 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1080 booth_recode_w7(&sign0, &digit0, wvalue); 1081 ecp_nistz256_avx2_select_w7((P256_POINT_AFFINE *) r, 1082 preComputedTable[36], digit0); 1083 ecp_nistz256_neg(tmp, r->Y); 1084 copy_conditional(r->Y, tmp, sign0); 1085 memcpy(r->Z, ONE, sizeof(ONE)); 1086 /* Sum the four windows */ 1087 ecp_nistz256_point_add(r, r, &res_point_arr[0]); 1088 ecp_nistz256_point_add(r, r, &res_point_arr[1]); 1089 ecp_nistz256_point_add(r, r, &res_point_arr[2]); 1090 ecp_nistz256_point_add(r, r, &res_point_arr[3]); 1091} 1092# endif 1093#endif 1094 1095static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, 1096 const P256_POINT_AFFINE *in, 1097 BN_CTX *ctx) 1098{ 1099 BIGNUM x, y; 1100 BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS]; 1101 int ret = 0; 1102 1103 memcpy(d_x, in->X, sizeof(d_x)); 1104 x.d = d_x; 1105 x.dmax = x.top = P256_LIMBS; 1106 x.neg = 0; 1107 x.flags = BN_FLG_STATIC_DATA; 1108 1109 memcpy(d_y, in->Y, sizeof(d_y)); 1110 y.d = d_y; 1111 y.dmax = y.top = P256_LIMBS; 1112 y.neg = 0; 1113 y.flags = BN_FLG_STATIC_DATA; 1114 1115 ret = EC_POINT_set_affine_coordinates_GFp(group, out, &x, &y, ctx); 1116 1117 return ret; 1118} 1119 1120/* r = scalar*G + sum(scalars[i]*points[i]) */ 1121static int ecp_nistz256_points_mul(const EC_GROUP *group, 1122 EC_POINT *r, 1123 const BIGNUM *scalar, 1124 size_t num, 1125 const EC_POINT *points[], 1126 const BIGNUM *scalars[], BN_CTX *ctx) 1127{ 1128 int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; 1129 size_t j; 1130 unsigned char p_str[33] = { 0 }; 1131 const PRECOMP256_ROW *preComputedTable = NULL; 1132 const EC_PRE_COMP *pre_comp = NULL; 1133 const EC_POINT *generator = NULL; 1134 unsigned int index = 0; 1135 BN_CTX *new_ctx = NULL; 1136 const BIGNUM **new_scalars = NULL; 1137 const EC_POINT **new_points = NULL; 1138 const unsigned int window_size = 7; 1139 const unsigned int mask = (1 << (window_size + 1)) - 1; 1140 unsigned int wvalue; 1141 ALIGN32 union { 1142 P256_POINT p; 1143 P256_POINT_AFFINE a; 1144 } t, p; 1145 BIGNUM *tmp_scalar; 1146 1147 if (group->meth != r->meth) { 1148 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); 1149 return 0; 1150 } 1151 1152 if ((scalar == NULL) && (num == 0)) 1153 return EC_POINT_set_to_infinity(group, r); 1154 1155 for (j = 0; j < num; j++) { 1156 if (group->meth != points[j]->meth) { 1157 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); 1158 return 0; 1159 } 1160 } 1161 1162 if (ctx == NULL) { 1163 ctx = new_ctx = BN_CTX_new(); 1164 if (ctx == NULL) 1165 goto err; 1166 } 1167 1168 BN_CTX_start(ctx); 1169 1170 if (scalar) { 1171 generator = EC_GROUP_get0_generator(group); 1172 if (generator == NULL) { 1173 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); 1174 goto err; 1175 } 1176 1177 /* look if we can use precomputed multiples of generator */ 1178 pre_comp = 1179 EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup, 1180 ecp_nistz256_pre_comp_free, 1181 ecp_nistz256_pre_comp_clear_free); 1182 1183 if (pre_comp) { 1184 /* 1185 * If there is a precomputed table for the generator, check that 1186 * it was generated with the same generator. 1187 */ 1188 EC_POINT *pre_comp_generator = EC_POINT_new(group); 1189 if (pre_comp_generator == NULL) 1190 goto err; 1191 1192 if (!ecp_nistz256_set_from_affine 1193 (pre_comp_generator, group, pre_comp->precomp[0], ctx)) { 1194 EC_POINT_free(pre_comp_generator); 1195 goto err; 1196 } 1197 1198 if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx)) 1199 preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp; 1200 1201 EC_POINT_free(pre_comp_generator); 1202 } 1203 1204 if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) { 1205 /* 1206 * If there is no precomputed data, but the generator 1207 * is the default, a hardcoded table of precomputed 1208 * data is used. This is because applications, such as 1209 * Apache, do not use EC_KEY_precompute_mult. 1210 */ 1211 preComputedTable = (const PRECOMP256_ROW *)ecp_nistz256_precomputed; 1212 } 1213 1214 if (preComputedTable) { 1215 if ((BN_num_bits(scalar) > 256) 1216 || BN_is_negative(scalar)) { 1217 if ((tmp_scalar = BN_CTX_get(ctx)) == NULL) 1218 goto err; 1219 1220 if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { 1221 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB); 1222 goto err; 1223 } 1224 scalar = tmp_scalar; 1225 } 1226 1227 for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) { 1228 BN_ULONG d = scalar->d[i / BN_BYTES]; 1229 1230 p_str[i + 0] = d & 0xff; 1231 p_str[i + 1] = (d >> 8) & 0xff; 1232 p_str[i + 2] = (d >> 16) & 0xff; 1233 p_str[i + 3] = (d >>= 24) & 0xff; 1234 if (BN_BYTES == 8) { 1235 d >>= 8; 1236 p_str[i + 4] = d & 0xff; 1237 p_str[i + 5] = (d >> 8) & 0xff; 1238 p_str[i + 6] = (d >> 16) & 0xff; 1239 p_str[i + 7] = (d >> 24) & 0xff; 1240 } 1241 } 1242 1243 for (; i < 33; i++) 1244 p_str[i] = 0; 1245 1246#if defined(ECP_NISTZ256_AVX2) 1247 if (ecp_nistz_avx2_eligible()) { 1248 ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable); 1249 } else 1250#endif 1251 { 1252 /* First window */ 1253 wvalue = (p_str[0] << 1) & mask; 1254 index += window_size; 1255 1256 wvalue = _booth_recode_w7(wvalue); 1257 1258 ecp_nistz256_select_w7(&p.a, preComputedTable[0], wvalue >> 1); 1259 1260 ecp_nistz256_neg(p.p.Z, p.p.Y); 1261 copy_conditional(p.p.Y, p.p.Z, wvalue & 1); 1262 1263 memcpy(p.p.Z, ONE, sizeof(ONE)); 1264 1265 for (i = 1; i < 37; i++) { 1266 unsigned int off = (index - 1) / 8; 1267 wvalue = p_str[off] | p_str[off + 1] << 8; 1268 wvalue = (wvalue >> ((index - 1) % 8)) & mask; 1269 index += window_size; 1270 1271 wvalue = _booth_recode_w7(wvalue); 1272 1273 ecp_nistz256_select_w7(&t.a, 1274 preComputedTable[i], wvalue >> 1); 1275 1276 ecp_nistz256_neg(t.p.Z, t.a.Y); 1277 copy_conditional(t.a.Y, t.p.Z, wvalue & 1); 1278 1279 ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); 1280 } 1281 } 1282 } else { 1283 p_is_infinity = 1; 1284 no_precomp_for_generator = 1; 1285 } 1286 } else 1287 p_is_infinity = 1; 1288 1289 if (no_precomp_for_generator) { 1290 /* 1291 * Without a precomputed table for the generator, it has to be 1292 * handled like a normal point. 1293 */ 1294 new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); 1295 if (!new_scalars) { 1296 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1297 goto err; 1298 } 1299 1300 new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); 1301 if (!new_points) { 1302 ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); 1303 goto err; 1304 } 1305 1306 memcpy(new_scalars, scalars, num * sizeof(BIGNUM *)); 1307 new_scalars[num] = scalar; 1308 memcpy(new_points, points, num * sizeof(EC_POINT *)); 1309 new_points[num] = generator; 1310 1311 scalars = new_scalars; 1312 points = new_points; 1313 num++; 1314 } 1315 1316 if (num) { 1317 P256_POINT *out = &t.p; 1318 if (p_is_infinity) 1319 out = &p.p; 1320 1321 if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx)) 1322 goto err; 1323 1324 if (!p_is_infinity) 1325 ecp_nistz256_point_add(&p.p, &p.p, out); 1326 } 1327 1328 /* Not constant-time, but we're only operating on the public output. */ 1329 if (!ecp_nistz256_set_words(&r->X, p.p.X) || 1330 !ecp_nistz256_set_words(&r->Y, p.p.Y) || 1331 !ecp_nistz256_set_words(&r->Z, p.p.Z)) { 1332 goto err; 1333 } 1334 r->Z_is_one = is_one(p.p.Z) & 1; 1335 1336 ret = 1; 1337 1338err: 1339 if (ctx) 1340 BN_CTX_end(ctx); 1341 BN_CTX_free(new_ctx); 1342 if (new_points) 1343 OPENSSL_free(new_points); 1344 if (new_scalars) 1345 OPENSSL_free(new_scalars); 1346 return ret; 1347} 1348 1349static int ecp_nistz256_get_affine(const EC_GROUP *group, 1350 const EC_POINT *point, 1351 BIGNUM *x, BIGNUM *y, BN_CTX *ctx) 1352{ 1353 BN_ULONG z_inv2[P256_LIMBS]; 1354 BN_ULONG z_inv3[P256_LIMBS]; 1355 BN_ULONG x_aff[P256_LIMBS]; 1356 BN_ULONG y_aff[P256_LIMBS]; 1357 BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; 1358 BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS]; 1359 1360 if (EC_POINT_is_at_infinity(group, point)) { 1361 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY); 1362 return 0; 1363 } 1364 1365 if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) || 1366 !ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) || 1367 !ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) { 1368 ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE); 1369 return 0; 1370 } 1371 1372 ecp_nistz256_mod_inverse(z_inv3, point_z); 1373 ecp_nistz256_sqr_mont(z_inv2, z_inv3); 1374 ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); 1375 1376 if (x != NULL) { 1377 ecp_nistz256_from_mont(x_ret, x_aff); 1378 if (!ecp_nistz256_set_words(x, x_ret)) 1379 return 0; 1380 } 1381 1382 if (y != NULL) { 1383 ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); 1384 ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); 1385 ecp_nistz256_from_mont(y_ret, y_aff); 1386 if (!ecp_nistz256_set_words(y, y_ret)) 1387 return 0; 1388 } 1389 1390 return 1; 1391} 1392 1393static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) 1394{ 1395 EC_PRE_COMP *ret = NULL; 1396 1397 if (!group) 1398 return NULL; 1399 1400 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); 1401 1402 if (!ret) { 1403 ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 1404 return ret; 1405 } 1406 1407 ret->group = group; 1408 ret->w = 6; /* default */ 1409 ret->precomp = NULL; 1410 ret->precomp_storage = NULL; 1411 ret->references = 1; 1412 return ret; 1413} 1414 1415static void *ecp_nistz256_pre_comp_dup(void *src_) 1416{ 1417 EC_PRE_COMP *src = src_; 1418 1419 /* no need to actually copy, these objects never change! */ 1420 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 1421 1422 return src_; 1423} 1424 1425static void ecp_nistz256_pre_comp_free(void *pre_) 1426{ 1427 int i; 1428 EC_PRE_COMP *pre = pre_; 1429 1430 if (!pre) 1431 return; 1432 1433 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1434 if (i > 0) 1435 return; 1436 1437 if (pre->precomp_storage) 1438 OPENSSL_free(pre->precomp_storage); 1439 1440 OPENSSL_free(pre); 1441} 1442 1443static void ecp_nistz256_pre_comp_clear_free(void *pre_) 1444{ 1445 int i; 1446 EC_PRE_COMP *pre = pre_; 1447 1448 if (!pre) 1449 return; 1450 1451 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 1452 if (i > 0) 1453 return; 1454 1455 if (pre->precomp_storage) { 1456 OPENSSL_cleanse(pre->precomp, 1457 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37); 1458 OPENSSL_free(pre->precomp_storage); 1459 } 1460 OPENSSL_cleanse(pre, sizeof *pre); 1461 OPENSSL_free(pre); 1462} 1463 1464static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) 1465{ 1466 /* There is a hard-coded table for the default generator. */ 1467 const EC_POINT *generator = EC_GROUP_get0_generator(group); 1468 if (generator != NULL && ecp_nistz256_is_affine_G(generator)) { 1469 /* There is a hard-coded table for the default generator. */ 1470 return 1; 1471 } 1472 1473 return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup, 1474 ecp_nistz256_pre_comp_free, 1475 ecp_nistz256_pre_comp_clear_free) != NULL; 1476} 1477 1478const EC_METHOD *EC_GFp_nistz256_method(void) 1479{ 1480 static const EC_METHOD ret = { 1481 EC_FLAGS_DEFAULT_OCT, 1482 NID_X9_62_prime_field, 1483 ec_GFp_mont_group_init, 1484 ec_GFp_mont_group_finish, 1485 ec_GFp_mont_group_clear_finish, 1486 ec_GFp_mont_group_copy, 1487 ec_GFp_mont_group_set_curve, 1488 ec_GFp_simple_group_get_curve, 1489 ec_GFp_simple_group_get_degree, 1490 ec_GFp_simple_group_check_discriminant, 1491 ec_GFp_simple_point_init, 1492 ec_GFp_simple_point_finish, 1493 ec_GFp_simple_point_clear_finish, 1494 ec_GFp_simple_point_copy, 1495 ec_GFp_simple_point_set_to_infinity, 1496 ec_GFp_simple_set_Jprojective_coordinates_GFp, 1497 ec_GFp_simple_get_Jprojective_coordinates_GFp, 1498 ec_GFp_simple_point_set_affine_coordinates, 1499 ecp_nistz256_get_affine, 1500 0, 0, 0, 1501 ec_GFp_simple_add, 1502 ec_GFp_simple_dbl, 1503 ec_GFp_simple_invert, 1504 ec_GFp_simple_is_at_infinity, 1505 ec_GFp_simple_is_on_curve, 1506 ec_GFp_simple_cmp, 1507 ec_GFp_simple_make_affine, 1508 ec_GFp_simple_points_make_affine, 1509 ecp_nistz256_points_mul, /* mul */ 1510 ecp_nistz256_mult_precompute, /* precompute_mult */ 1511 ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */ 1512 ec_GFp_mont_field_mul, 1513 ec_GFp_mont_field_sqr, 1514 0, /* field_div */ 1515 ec_GFp_mont_field_encode, 1516 ec_GFp_mont_field_decode, 1517 ec_GFp_mont_field_set_to_one 1518 }; 1519 1520 return &ret; 1521} 1522